According to James C. Bennett, for these countries/cultures to be included under the Anglosphere umbrella is not only speaking English, but also adhering to some shared set of history or mores (whether this is colonial influence or not doesn't seem to matter). This shared history includes thought embodied in the Magna Carta, Bill of Rights, and other such documents considered "Western in origin". To be an Anglospherist one must recognize:

Networked, rather than hierarchical, structure - The relationship between America, Scotland, Ireland, and Brittain as an example may have been contested historically but stands today as a "Great Britain" and a "United States", moving beyond the hierachical 'King-kingdom' and 'Colony-colonized'. "...Anglospherists call on all English-speaking nations to abandon Haushoferian fantasies of geographical blocs: on America to downgrade its hemispherist ambitions, on Britain to rethink its Europeanist illusions, and on Australia to reject its 'Asian identity' fallacy..."

Memetic, rather than genetic, identity - the Melting Pot encompasses a huge range of racial diversity but all members are part of an Anglophone society. The cultural diversity of this population is an inherent feature of the Anglosphere, but...

Emphasis is placed on similarities with recognition of differences - You are British, I am American, but we are both innocent until proven guilty.

Some areas are noted to be "on the fringe" or the Anglosphere (such as India or Japan) because of differing historical points of view. India has a large cross-section of English speakers due to colonial rule. Japan has a cross-section of English speakers from American post-war activities (reinforced by the national education apparatus and Western business culture). The race or history of a group does not exclude them from the Anglosphere however, and as time and diffusion goes on India will likely move closer to the core. I suspect Japan will remain on the outer-shell due to (albeit changing) cultural-xenophobia and a sense of collectivism over individuality.

Since "Anglospherism is assuredly not the racialist Anglo-Saxonism dating from the era around 1900, nor the sentimental attachment of the Anglo-American Special Relationship of the decades before and after World War II..." the spread of the Anglosphere to other regions is hindered in this modern era by technical literacy and access to the Internet. The only counter argument is that computerized translation technology will reach a point of sophistication that The Web will have no determinable predominate language.

Sources:

"An Anglosphere Primer" by James C. Bennett can be found at
http://www.pattern.com/bennettj-anglosphereprimer.html